Filament-motor protein system under loading: instability and limit cycle oscillations

TL;DR

This paper models the dynamics of a filament interacting with motor proteins under load, revealing conditions for instability and oscillations, and uses both analytical and numerical methods to understand these behaviors.

Contribution

It introduces a mean field model for filament-motor interactions under load, demonstrating the emergence of limit cycle oscillations via a Hopf bifurcation.

Findings

Transition from stable to unstable filament configurations under load

Emergence of limit cycle oscillations with elastic loading

Good agreement between simulations and mean field predictions

Abstract

We consider the dynamics of a rigid filament in a motor protein assay under external loading. The motor proteins are modeled as active harmonic linkers with tail ends immobilized on a substrate. Their heads attach to the filament stochastically to extend along it, resulting in a force on the filament, before detaching. The rate of extension and detachment are load dependent. Here we formulate and characterize the governing dynamics in the mean field approximation using linear stability analysis, and direct numerical simulations of the motor proteins and filament. Under constant loading, the system shows transition from a stable configuration to instability towards detachment of the filament from motor proteins. Under elastic loading, we find emergence of stable limit cycle oscillations via a supercritical Hopf bifurcation with change in activity and the number of motor proteins. Numerical simulations of the system for large number of motor proteins show good agreement with the mean field predictions.